An Algorithm to Discover the k-Clique Cover in Networks

  • Authors:
  • Luís Cavique;Armando B. Mendes;Jorge M. Santos

  • Affiliations:
  • University Aberta, Lisboa, Portugal 1269-001;University of Azores, Ponta Delgada, Portugal 9501-801;University of Evora, Evora, Portugal 7000

  • Venue:
  • EPIA '09 Proceedings of the 14th Portuguese Conference on Artificial Intelligence: Progress in Artificial Intelligence
  • Year:
  • 2009

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Abstract

In social network analysis, a k-clique is a relaxed clique, i.e., a k-clique is a quasi-complete sub-graph. A k-clique in a graph is a sub-graph where the distance between any two vertices is no greater than k. The visualization of a small number of vertices can be easily performed in a graph. However, when the number of vertices and edges increases the visualization becomes incomprehensible. In this paper, we propose a new graph mining approach based on k-cliques. The concept of relaxed clique is extended to the whole graph, to achieve a general view, by covering the network with k-cliques. The sequence of k-clique covers is presented, combining small world concepts with community structure components. Computational results and examples are presented.